Problem: Solve for $f$. Give an exact answer. $9f=\dfrac12\left(12f-2\right)$ $f =$
Solution: We need to manipulate the equation to get $ f $ by itself. $\begin{aligned} 9f &= \dfrac12\left(12f-2\right) \\\\ 9f &= 6f-1~~~~~~~~~~\gray{\text{Distribute}}\\\\ 9f{-6f} &= 6f-1{-6f} ~~~~~~~~~~\gray{\text{Subtract 6f from each side}}\\\\ 3f &=-1 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{3f}{{3}}&= \dfrac{-1}{{3}}~~~~~~~~~~\gray{\text{Divide each side by 3}} \\\\ f &= {-\dfrac13} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ f = { -\dfrac13 }~~~~~~~~$ [Let's check our work!]